The potential energy surface (PES) of the H-3(+) ground state is computed by means of the single and double excitation configuration interaction with an explicit linear r(12) term in the wave function (CISD-R12) developed recently by the present authors, with a nearly saturated basis set. The points of the PES suggested by Meyer, Botschwina, and Burton (MBB) were chosen and the fitting procedure of the same authors was followed. The present PES has both on an absolute and a relative scale (i.e., relative to the minimum) an error of a few microhartrees (mu E(h)) in the relevant region, an accuracy that has never before been achieved in a quantum chemical calculation for a triatomic molecule. From the fit the vibrational term values for the fundamental bands and some overtones of H-3(+), H2D+, HD2+, and D-3(+) were computed by means of the TRIATOM package of Tennyson and Miller. The computed frequencies are in better agreement with experiment (maximum error similar to 0.5 cm(-1)) than those of all previous ab initio calculations (without empirical adjustment). To achieve this accuracy, it is necessary to go beyond the Born-Oppenheimer approximation and to take care of the finite mass ratio between nuclei and electrons.